NYU Researchers Solve Feynman’s Century-Old Reverse Sprinkler Mystery

Researchers at New York University’s Courant Institute Resolve the Long-Standing “Feynman’s Sprinkler Problem”

Researchers at New York University’s Courant Institute have identified the physical mechanisms behind the “reverse sprinkler” phenomenon, a long-standing puzzle in fluid dynamics. A new paper published in the Proceedings of the National Academy of Sciences provides a definitive explanation for the behavior of these devices, which have challenged physicists since the mid-20th century. By constructing a device that draws water inward rather than spraying it outward, the researchers observed how the system interacts with its environment to produce motion.

Historical Context of the Reverse Sprinkler

The reverse sprinkler problem is associated with physicist Richard Feynman because he popularized the concept, but it actually dates back to a chapter in Ernst Mach’s 1883 textbook, The Science of Mechanics (Die Mechanik in Ihrer Entwicklung Historisch-Kritisch Dargerstellt). Mach’s thought experiment languished in relative obscurity until a group of Princeton University physicists began debating the issue in the 1940s. Feynman was a graduate student there at the time and threw himself into the debate with gusto, even devising an experiment in the cyclotron laboratory to test his hypothesis.

One might intuit that a reverse sprinkler would work just like a regular sprinkler, merely played backward. However, the physics proves more complicated. As Feynman wrote in his 1985 memoir, Surely You’re Joking, Mr. Feynman!: The answer is perfectly clear at first sight. The trouble was, some guy would think it was perfectly clear [that the rotation would be] one way, and another guy would think it was perfectly clear the other way.

Mach proposed that there would be no rotation with a reverse sprinkler, theorizing that the reaction force on the nozzle as it sucks in water pulls the nozzle counter-clockwise, while the water flowing into the inside of the nozzle pushes it clockwise. In this steady-state scenario, Mach argued the two forces would cancel each other out. Feynman’s own experiment showed a slight tremor when pressure was first applied to pump water through the nozzle, and then the sprinkler returned to its original position and remained still.

Experimental Breakthroughs

The research team at NYU utilized a specialized apparatus to measure the forces at play when a sprinkler functions in reverse. While a standard sprinkler rotates due to the momentum of water exiting its nozzles, the reverse sprinkler—which pulls fluid into its arms—exhibits a more complex interaction between internal flow and external resistance. The scientists found that the device’s rotation depends on the specific way the fluid enters the system and how the surrounding medium reacts to that intake. These findings clarify the role of fluid inertia and pressure gradients in determining the direction and speed of the device’s movement.

“This work provides the experimental answer for Feynman’s Sprinkler Problem by showing, across several sprinkler types, how the angular momentum of water flows drives sprinklers’ rotation,” said senior author Leif Ristroph, an associate professor at New York University’s Courant Institute School of Mathematics, Computing, and Data Science.

This study is not the team’s first work on the problem, as it builds on what they reported in an earlier 2024 paper. Unlike Feynman himself, the researchers managed to make their reverse sprinkler rotate. The significance of the work extends well beyond an esoteric question about a hypothetical device, providing new insights into the physics of fluid dynamics. During his lifetime, Feynman discouraged naming the problem after himself, noting that it built upon ideas first explored by physicist Ernst Mach in the 1880s.

Future Engineering Implications

The research provides a firmer understanding of how components respond to fluid flows. “Our findings provide a firmer understanding of how components respond to fluid flows—knowledge that can guide future engineering and technological advances for devices, such as turbines, that convert these flows into energy,” said co-author Brennan Sprinkle, an assistant professor at Colorado School of Mines.

By identifying the physical mechanisms behind the reverse sprinkler, the team has effectively resolved the debate surrounding the mechanics of reverse-flow systems. The study confirms that the system’s interaction with its environment is key to producing motion, settling a question that has persisted in the field of physics for decades.